Leseprobe
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Asymptotics of Elliptic and Parabolic PDEs
Zeev Schuss, David Holcman
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Springer International Publishing 
Naturwissenschaften, Medizin, Informatik, Technik / Analysis
Beschreibung
This is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biological and physical sciences.
In more detail, the book presents the analytic methods and tools for approximating solutions of mixed boundary value problems, with particular emphasis on the narrow escape problem. Informed throughout by real-world applications, the book includes topics such as the Fokker-Planck equation, boundary layer analysis, WKB approximation, applications of spectral theory, as well as recent results in narrow escape theory. Numerical and stochastic aspects, including mean first passage time and extreme statistics, are discussed in detail and relevant applications are presented in parallel with the theory.
Including background on the classical asymptotic theory of differential equations, this book is written for scientists of various backgrounds interested inderiving solutions to real-world problems from first principles.
Kundenbewertungen
Green’s functions, long-time asymptotics, Ray method, narrow escape, eigenvalues, partial differential equations, matched asymptotics, short-time asymptotics, applied conformal transformation, Poisson-Nernst-Planck, Eikonal equation, Neumann’s function, non-self adjoint operators, boundary value problems, Helmholtz equation, first passage times, WKB, extreme statistics, integral equations, asymptotic formula